Pentavalent vertex-transitive diameter two graphs

doi:10.1007/s11464-016-0617-9

Front. Math. China

2017, Vol. 12

Issue (2) : 377-388 https://doi.org/10.1007/s11464-016-0617-9

RESEARCH ARTICLE

Pentavalent vertex-transitive diameter two graphs

Wei JIN(

)

School of Statistics; Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China

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Abstract

We classify the family of pentavalent vertex-transitive graphs $Γ$ with diameter 2. Suppose that the automorphism group of $Γ$ is transitive on the set of ordered distance 2 vertex pairs. Then we show that either $Γ$ is distance-transitive or $Γ$ is one of $C 8 ¯, K 5 □ K 2, C 5 [K 2], 2 C 4 ¯, or K 3 □ K 4$ .

Keywords vertex-transitive graph diameter automorphism group

Corresponding Author(s): Wei JIN

Issue Date: 27 December 2016

Cite this article:

Wei JIN. Pentavalent vertex-transitive diameter two graphs[J]. Front. Math. China, 2017, 12(2): 377-388.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0617-9
https://academic.hep.com.cn/fmc/EN/Y2017/V12/I2/377

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